I had the best parents in the world and they used their open hands, yardsticks, and my dad's belt to keep us in line. If we spoke unclean language, the insides of our mouths were washed with soap. If we misbehaved at school, we knew there would be severe punishment at home.
That said, I do believe that a little preschooler should not be struck the way it appeared Martha was.
I'm with you. A belt or a switch or a yardstick is OK with me. But wailing away in a parking lot is too scary. She could have done some damage if she hit the right spot.